3 Reasons the Pope Should NOT Sell the Vatican's Art to Feed the Poor.

Have you ever been confronted by Protestants or secularists (both of which groups, incidentally, do less for the poor than the Catholic Church) who dismiss the Church because it has priceless works of art saying the pope ought to sell them off to feed the poor? Vatican Museum director Antonio Paolucci has and he as a simple reply,

“because man would be poorer in every sense”. (source)

 
1. Spiritual Poverty is Worse than Material Poverty
In other words, "man shall not live by bread alone" (cf. Matt 4:4). The artworks of the Vatican are the preserve of all the world and all of us would be immeasurably poorer if they were to be sold to some private collector, never to be enjoyed by the Faithful again. The great artists that made these masterpieces made them to honor and glorify God and to save the souls of those who, through viewing them, would grow closer to God and who would be brought to repentance for their sins. Having once stood in front of Michelangelo's Last Judgement as an unbeliever, I can personally testify the power good art can work upon a even a closed and dry soul. It is this poverty, spiritual poverty, which Mother Teresa (who lived and labored among the economically poorest of the world) called "the worst poverty and the most difficult to overcome." (source) 

2. What Would Jesus Do?
The attitude of the man who wants to sell off man's patrimony for a few loaves of bread isn't anything new, Jesus Himself faced such an objection from within His chosen apostles

Six days before the Passover, Jesus came to Bethany, where Laz′arus was, whom Jesus had raised from the dead.  There they made him a supper; Martha served, and Laz′arus was one of those at table with him.  Mary took a pound of costly ointment of pure nard and anointed the feet of Jesus and wiped his feet with her hair; and the house was filled with the fragrance of the ointment.  But Judas Iscariot, one of his disciples (he who was to betray him), said,  “Why was this ointment not sold for three hundred denarii and given to the poor?” (Jn 12: 1-5)

To Judas, the progenitor of our modern critic, Jesus has no kind words,

“Let her alone; why do you trouble her? She has done a beautiful thing to me" (Mk 14:6)

 As too have the greatest artists in the history of man, who have spent their time and treasure doing "beautiful things" not for overly wealthy private art collectors, but for Him.

Jesus then goes on to point out the ultimate futility of trying to sell off all things of beauty for bread, reminding His disciples that

 "The poor you always have with you” (Jn 12:8)

We will never eliminate poverty this side of the parousia and despoiling God's house in a vain effort to is clearly not commended by Christ. 

3. God Doesn't Will It
In fact, it seems God (as can be seen in His plans for both the Tabernacle in the Wilderness and the Temple of Solomon) isn't a big fan of depriving His people of beauty,

The house which King Solomon built for the Lord was sixty cubits long, twenty cubits wide, and thirty cubits high....lined the walls of the house on the inside with boards of cedar... He built twenty cubits of the rear of the house with boards of cedar from the floor to the rafters, and he built this within as an inner sanctuary, as the most holy place....The cedar within the house was carved in the form of gourds and open flowers; all was cedar, no stone was seen.  The inner sanctuary he prepared in the innermost part of the house, to set there the ark of the covenant of the Lord.  The inner sanctuary was twenty cubits long, twenty cubits wide, and twenty cubits high; and he overlaid it with pure gold. He also made an altar of cedar. And Solomon overlaid the inside of the house with pure gold, and he drew chains of gold across, in front of the inner sanctuary, and overlaid it with gold. And he overlaid the whole house with gold, until all the house was finished. Also the whole altar that belonged to the inner sanctuary he overlaid with gold.  In the inner sanctuary he made two cherubim of olivewood, each ten cubits high.... And he overlaid the cherubim with gold.He carved all the walls of the house round about with carved figures of cherubim and palm trees and open flowers, in the inner and outer rooms.  The floor of the house he overlaid with gold in the inner and outer rooms. (1 Kings 6) 

A False Dichotomy 
 None of that, of course, is to downplay the importance of feeding the hungry (something Jesus also demands)

‘Depart from me, you cursed, into the eternal fire prepared for the devil and his angels; 42 for I was hungry and you gave me no food...‘Truly, I say to you, as you did it not to one of the least of these, you did it not to me." (Matt 25)

Which ends up being another example of the classic Catholic principal of "both/and" not "either/or" (which is the hallmark of heresy). We are not called to either beautiful churches or feeding the poor, but to both beauty and charity. For, in the final analysis, beauty is a form of charity, it is feeding the spiritually poor.

The Best Answer
But maybe the best answer is to ask whoever raises this objection which of their personal effects they're in the process of selling to feed the poor. For some reason I doubt their BMW, shoe closet, golf clubs, iPhone, etc is doing much to alleviate the spiritual poverty of the world, unlike the Vatican's art.